D 0 E- HTG R-90 40 6 Revision 0

This technical report i clearance and no furth the report without prior

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MHTGR NUCLEAR PHYSICS BENCHMARKS

Issued By: General Atomics P.O. Box85608

San Diego, California 92186-9784

DOE CONTRACT DE-AC03-89SF 17885

GA Project 6300

FEBRUARY 1994

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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DOE-HTGR-90406 / Rev. 0 I

ABSTRACT

This report defines a series of core physics calculational benchmark problems for the Modular High Temperature Gas-Cooled Reactor (MHTGR). These benchmark problems are specified for a realistic MHTGR core to facilitate comparison of calculational results from different computational methods to be performed by various participating organizations. These analytical comparisons will be used to confm the accuracy of the computational methods used for MHTGR physics analysis, as part of the code validation process. These analytical benchmark problems are specified based on an annular core containing 84 columns with a high WD ratio, and include the dimensions, temperatures, and nuclide atom densities for a series of core models of increasing complexity, including 1-D radial, 1-D axial, 2-D radial hexagonal (1 hex per element), 2-D radial subhex (7 hexes per element), 3-D hexagonal, and 3-D subhex models. A time point at the beginning of the initial cycle is used for these benchmark problems to simplify the calculations. The nuclear analyst must use the data provided to create appropriate multigroup diffusion cross sections, accounting for the heterogeneity in the fuel particles and rods, along with the fixed burnable poison (FBP) and control rods. Benchmark cases to be analyzed include the hot (100% power) and cold (300 K) reactor with and without moisture ingress, for all-rods-out and all-rods- in configurations. Power distributions and core K-eff values are to be calculated for each case, while total rod worth, moisture ingress worth, and cold-to-hot temperature defect are derived from case-to-case differences in core reactivity. Conclusions regarding the MHTGR computational methods that are based on these MHTGR benchmark problems should also apply to other core sizes and power levels because the basic geometries and materials will remain the same.

iv DOE-HTGR-90406 / Rev. 0

CONTENTS

ABSTRACT ........................................................................................... iv

LIST OF TABLES .................................................................................... .. LIST OF FIGURES ................................................................................. ... LIST OF ABBREVIATIONS AND ACRONYMS ............................................ vu

1 . INTRODUCIION AND SUMMARY ...................................................... 1-1

2 . CORE! DESIGN DESCRIPTION ............................................................ 2-1 2.1 Core Configuration ...................................................................... 2-1 2.2 Fuel Element Design .................................................................... 2. 1 2.3 Fuel Design .............................................................................. 2.5 2.4 Reflector Element Design ............................................................... 2-5 2.5 Control Material ......................................................................... 2. 10

3 . MIITGR BENCHMARK PROBLEMS .................................................... 3-1 3.1 Benchmark Calculations to be Perfonned ........................................... -3-1 3.2 Calculation of Cross Sections .......................................................... 3-3

3.2.1 Core Cross Sections .......................................................... 3.3 3.2.2 Reflector Cross Sections ..................................................... 3.7 3.2.3 Shielded FBP Cross Sections ................................................ 3-7 3.2.4 Shielded Control Rod Cross Sections ...................................... 3.9 Specification of Models for Benchmark Calculations ............................... 3.9 3.3.1 1-D Radial Model .............................................................. 3-11 3.3.2 1-D Axial Model ............................................................... 3-14 3.3.3 2-D Hexagonal Model ........................................................ 3. 14 3.3.4 2-D Subhex Model ............................................................ 3.23 3.3.5 3-D Hexagonal Model ........................................................ 3.30 3.3.6 3-D Subhex Model ............................................................ 3.32

3.3

V DOE-HTGR-90406 / Rev . 0

LIST OF TABLES

TABLE

2- 1 2-2 3- 1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 3-10 3-1 1 3-12 3-13 3- 14 3- 15

TITLE PAGE

Design Parameters for MHTGR Benchmarks .................................. 2.4 Element and Core Volumes ....................................................... 2.8 MHTGR Benchmark Calculations to be Performed ........................... 3.2 Data for the Calculation of Dry Core Cross Sections .......................... 3.5 Data for Calculation of Reflector Cross Sections ............................... 3-8 Data for 1-D FBP Cell Calculation ............................................... 3.8 Data for 1-D Control Rod Cell Calculation ..................................... 3-10 Data for a 1-D Radial Benchmark ............................................... 3. 13 Atom Densities for 1-D Axial Benchmark ...................................... 3-16 Temperatures for 1-D Axial Benchmark ........................................ 3-17 Atom Densities for 2-D Hexagonal Benchmark ............................... 3-20 Temperatures and Control Rads for 2-D Hexagonal Benchmark ........... 3.22 Core Atom Density Types for 2-D Subhex Benchmark ...................... 3.26 Core Atom Densities for 2-D Subhex Benchmark ............................ 3.27 Reflector Atom Densities for 2-D Subhex Benchmark ....................... 3-28

Axial Zoning Factors and Control Rods for 3-D Hexagonal Benchmark . . 3.31 Temperatures and Control Rods for 2-D Subhex Benchmark ............... 3.29

vi DOE-HTGR-90406 / Rev . 0

LIST OF FIGURES

FIGURE TITLE PAGE

2- 1 2-2 2-3 2-4 2-5 2-6 3- 1 3-2 3-3 3-4 3-5 3-6 3-7

Reactor Elevation View ............................................................. 2-2 MHTGR Core Arrangement ....................................................... 2.3 Standard Fuel Element .............................................................. 2-6 Control or Reserve Shutdown Fuel Element ..................................... 2-7 Fuel Element Components ......................................................... 2.9 Reflector Control Element ......................................................... 2.11 120" Model of the 84 Column Core ............................................... 3-4 Model For 1 -D Radial Benchmark Calculations ................................ 3. 12 Model for 1-D Axial Benchmark Calculations .................................. 3. 15 Element Locations for Hexagonal Benchmarks ................................ 3. 18 Element Types for Hexagonal Benchmarks ..................................... 3-19 Subhex Geometry Used to Model an Element .................................. 3.24 Geometry for Subhex Benchmarks .............................................. 3.25

vii DOE-HTGR-90406 / Rev . 0

LIST OF ABBREVIATIONS AND ACRONYMS

BOIC

FBP

LEU

MHTGR

NU

RSC

V&V

Beginning of Initial Cycle

Fixed Burnable Poison

Low Enriched Uranium (~20% U-235)

Modular High Temperature Gas-Cooled React01

Natural Uranium

Reserve Shutdown Control

Verification and Validation

viii DOE-HTGR-90406 / Re\

1. INTRODUCTION AND SUMMARY

The nuclear physics design of the core of the Modular High Temperature Gas-Cooled Reactor (MHTGR) requires the use of verified and validated computational methods for the calculation of core physics parameters. To complete the verification and validation (V&V) of the MHTGR computational methods, it must be proven that the computational methods calculate certain physics parameters within acceptable uncertainty criteria. The physics parameters, and their uncertainty criteria (two sigma standard deviation) that is required to be satisfied for V&V, addressed by the proposed benchmark problems are as follows: temperature defect (&20%), control rod worth (f20%), power distribution (*15%), K-eff (&1.5%), and water ingress ( s 5 % ) . One method planned to be used for V&V of the MHTGR computational methods is to use the computational methods to calculate results of physics experiments performed in facilities that are as similar as possible to the MHTGR. To supplement this approach, and to enhance the confidence level regarding the accuracy of the MHTGR core physics computational methods, a series of core physics benchmark problems for the MHTGR are specified in this document. These benchmark problems are specified for a realistic MHTGR core to facilitate comparison of calculational results from different computational methods (diffusion theory, transport theory, Monte Carlo) to be performed by various participating organizations. These analytical comparisons will be used to confm the accuracy of the computational methods used for MHTGR physics analysis, as part of the code validation process. Calculational comparisons include temperatw defect, control rod worth, power distribution, K-eff, and water ingress. Other physics data required for V&V of MHTGR computational methods (fuel burnup, decay heat, and reactor transients) are not currently included in this set of benchmark problems.

These analytical benchmark problems are specified based on a reference design 450 MW(t) MHTGR, with an annular core containing 84 columns, at the beginning of the initial cycle (BOIC). The active core is an annulus of three rows of fuel elements with 10 fuel elements / column, surrounded by inner (central) and outer radial reflectors, and axial reflectors above and below the core. The annular core contains 12 control rods and 12 reserve shutdown control (RSC) holes, and the outer reflector contains 24 control rods. The fuel is composed of 19.8% low enriched uranium (LEU) fissile particles and natural uranium (NU) fertile particles. This configuration for the MHTGR benchmark problems is representative of recent design iterations for the MHTGR.

1-1 DOE-HTGR-90406 / Rev. 0

Section 2 provides a description of the core components which must be accounted for in realistic MHTGR core physics calculations. The information in this section provides the basis for the values provided in Section 3 for the benchmark problems. Section 2 also provides the data needed to create more detailed representations of the MHTGR benchmark problems than is provided in Section 3, such as with Monte Carlo methods using general combinatorial geometry.

Section 3 defines the analytical benchmark problems for a series of MHTGR core models of increasing complexity, including a 1-D radial benchmark, a 1-D axial benchmark, a 2-D hexagonal (1 hedelement) benchmark, a 2-D subhex (7 hexedelement) benchmark, a 3-D hexagonal benchmark, and a 3-D subhex benchmark. Dimensions, temperatures, and initial cycle atom densities are provided for all core locations in each of the benchmark problem models. The benchmark problems defined for all models include the hot (100% power) and cold (300 K) reactor for the all-rods-out condition, with and without moisture ingress. The 2-D and 3-D benchmark problems also include all-rods-in cases analogous to the above all-rods-out problems. The power distribution and K-effective value are to be calculated for as many benchmark problems as possible. Case-to-case comparisons yield the cold-to-hot temperature defects, moisture ingress reactivity worths, and total control rod worths. Additional K-eff data can come from the 0-D cross section calculation. Although an R-2 MHTGR model is not explicitly described, the nuclear analyst can construct an R-Z model if necessary from the 1-D radial and 1-D axial models.

The nuclear analyst must use the data provided in Sections 2 and 3 for his calculation of the MHTGR benchmark problems. The analyst's work will include choosing an appropriate multi- group neutron energy structure, and calculating multi-group cross sections which account for the heterogeneous structure of the core that has been homogenized in each of the benchmark models. Of primary concern is properly accounting for the grain and rod structure of the fuel, and the fixed burnable poison (FBP) and control rod strong absorber regions. Section 3.2 provides more detailed input data for constructing transport cell models of the FBP and control rods. Transverse leakages for the 1-D and 2-D radial models can be accounted for based upon the direct leakage results of the 1-D axial model. Conversely, the axial 1-D model can use the radial leakages from one of the various radial benchmark models to account for its transverse leakage. 3-D model results may also be used to account for 1-D and 2-D model transverse leakage.

Assumptions are made in the specification of the MHTGR benchmark problems relative to the actual core so that the benchmarks can be specified precisely without excessive detail, and to simplify the benchmarks so that they are relatively easy and straight-forward to calculate. This

1-2 DOE-HTGR-90406 / Rev. 0

should help to minimize errors in the calculation of the benchmarks, and should allow their calculation using existing computational methods within reasonable limits of time and funding. The impact of these assumptions on the calculated results should be small, so that the calculational differences obtained for the benchmark calculations should be usable for V&V of the MHTGR computational methods. The assumptions are listed below so that they can be considered further if necessary :

1.

2.

3.

4.

5 .

6.

7.

The average of five fixed burnable pins in the corners of the core element are modeled as seven FBP pins in each block, with one FBP pin in the center of each subhex. The FBP pins are therefore reduced in diameter to maintain the correct FBP volume fraction.

The regions of the radial and axial reflectors that are beyond the inside edge of the borated steel pins in the reflectors are ignored. The zero flux boundary condition ignores neutrons returning from these regions.

By homogenization of the graphite in the core and reflector blocks, neutron streaming in the gaps, coolant holes, and control holes is ignored.

Element bowing due to temperature gradients is ignored.

Uniform temperatures in the various regions are assumed, which ignores the details of the actual temperature distributions. For example, the fuel particles, fuel rod, and the block graphite are assumed to be at the same temperature, whereas in reality the fuel particles are at a higher temperature than the fuel rods, and the fuel rods are at a higher temperature than the block graphite. Also, in reality the temperatures in the core increase from the top of the core to the bottom of the core, because the coolant moves through the core from the top to the bottom.

Axial dimensions in the element are simplified: the length of the fuel rods and the fixed burnable poison rods are assumed to be identical to the height of the block, and the axial details of the control rods are ignored and replaced with a simple cross-sectional model across the B4C compact in the control rad.

In the suggested methodology for calculating the core cross sections, it is assumed that the particles and the fuel rods can be effectively homogenized into the block graphite by using homogenized core cross sections, it is assumed that the particle coatings can be homogenized

1-3 DOE-HTGR-90406 / Rev. 0

into the fuel rod matrix, it is assumed that the cross sections need not be position or temperam dependent, and it may be assumed that core leakage can be ignored in the calculation of the fine group spectrum used to collapse down to the broad group cross sections.

8. It is assumed that the reflector cross sections can be independent of position, and calculated for constant temperatures.

9. It is assumed that all uncertainties and variations in masses, dimensions, and temperatures can be ignored.

10. It is assumed that impurities can be simulated by homogenized B-10.

The benchmark models, with the simplifying assumptions stated above, are very similar to the models that are routinely used at General Atomics for MHTGR core design. Conclusions regarding the MHTGR computational methods that are based on these reference 450 MW(t) 84 column h4HTGR benchmark problems should also apply to other core sizes and power levels because the basic geometries and materials will remain the same.

This document is safety related, since it relates to V&V of core physics codes that are used to calculate safety related physics parameters, such as K-eff, power distributions, control rod worths, temperature defects, and reactivity effects of water ingress.

1-4 DOE-HTGR-90406 / Rev. 0

2. CORE DESIGN DESCRIPTION

Described below is the design for the core, elements, compacts, particles, fixed burnable poison (FBP), and reflectors used in the nuclear physics benchmark calculations specified in section 3.0. These benchmark calculations are specified based on a reference MHTGR design with 84 columns and a power level of 450 MW(t).

2.1 CORE CONFIGURATION

The reactor core consists of hexagonal graphite fuel and reflector elements, plenum elements, and reactivity control material, all located inside a reactor pressure vessel. A core elevation view is shown in Fig. 2-1 and a plan view is shown in Fig. 2-2. The left side of Fig. 2-1 is a cut from the Center of the core through the corners of the elements. The right side of Fig. 2- 1 is a cut from the center of the core through the flats of the elements.

The active core consists of hexagonal graphite fuel elements containing blind holes for fuel compacts and full length channels for helium coolant flow. The fuel elements are stacked to form columns (10 fuel elements per column) that rest on support structures as shown in Fig. 2- 1. The active core columns form a three row annulus, with columns of hexagonal graphite elements in the inner and outer reflector regions (see Fig. 2-2). Twelve core columns and 24 outer reflector columns contain channels for control rods. Twelve columns in the core also contain channels for reserve shutdown control (RSC) material. Axially above and below the fueled core elements are the replaceable axial reflector elements. Radially outside of the outer replaceable reflector elements are the permanent reflector blocks.

Basic core nuclear design parameters are summarized in Table 2-1.

2.2 FUEL ELEMENT DESIGN

There are three types of elements that contain fuel: standard elements, reserve shutdown elements that contain a channel for reserve shutdown control, and control elements that contain a control rod channel. The principal structural material of the fuel elements is graphite in the form of a right hexagonal prism 793.0 mm (31.22 in.) high and 361.0 mm (14.212 in.) across the flats,

2- 1 DOE-HTGR-90406 / Rev. 0

UPPER PLENUM SHROUD

UPPER CORE RESTRAINT ELEMENTS

' PERMANENT SIDE REFLECTOR

METALL IC CORE SUPPORT (BARREL)

' GRAPH I TE CORE SUPPORT ASSEMBLY

METALLIC CORE SUPPORT (FLOOR)

FIGURE 2-1 REACTOR ELEVATION VIEW

2-2 DOE-HTGR-90406 / Rev. 0

FIGURE 2-2 MHTGR CORE ARRANGEMENT

2-3 DOE-HTGR-90406 / Rev. 0

TABLE 2-1 DESIGN PARAMETERS FOR MHTGR BENCHMARKS

Core Power, MW(t) Core Columns Number of Fuel Elements (lO/column)

Standard Control Reserve shutdown

Number of Control Rods Inner reflector In-COE Outer reflector

Flat-to-flat dimension, including gaps between elements Height

Number of Reserve Shutdown Control Channels in the Core Hexagonal Fuel Element Dimensions, m (in.)

Active Core Height, m (in.) Fissile Material in Kernel (19.8% enriched U) Fertile Material in Kernel (natural U) Control Rod Hole Diameter, mm (in) RSC Hole Diameter, mm (in) Coolant Holes Per Element, small / large

Standard Element Control and RSC Element

Coolant Hole Diameter, mm (in) Small Large

Hole pitch between coolant and fuel holes, mm (in) FBP Holes Per Element FE3P Hole Diameter, mm (in) FBP Rods Per Element, average # FBP Rod Diameter, mm (in)

Length, m (in) Fuel Holes, Under Dowels/ Not Under Dowels

Standard Element Control and RSC Elements

Fuel Hole Diameter, mm (in) Fuel Compact Diameter, mm (in)

450 84

600 120 120

0 12 24 12

0.3610 (14.212) 0.7930 (31.22) 7.93 (312.2) uc0.2901.63 uc0.290 1.63 101.6 (4.0)

95.25 (3.75)

6/102 7/88

12.70 (0.50) 15.88 (0.625) 18.80 (0.74)

6 12.70 (0.50)

5 11.43 (0.45)

.7214 (28.40)

24/186 2411 62

12.70 (0.50) 12.45 (0.49)

2-4 DOE-HTGR-90406 / Rev. 0

including the gaps between the elements. The standard fuel element, shown in Fig. 2-3, contains an essentially continuous pattern of fuel and coolant holes in a triangular array. Exceptions are the central handling hole, which is surrounded by smaller coolant holes, and six corner holes available for fixed burnable poison (FBP) compacts. The reserve shutdown and control fuel elements differ from the standard fuel elements in that they contain 95.3 mm (3.75 in.) and 101.6 mm (4.0 in.) diameter channels, respectively (see Fig. 2-4). Those channels replace 24 fuel and 11 coolant holes. The pitch of the coolant and fuel hole array is 18.8 mm (0.74 in.).

The element design data was used to calculate the volume of the components in the standard, control, and RSC elements, and the volumes, and volume fractions for the entire core. Table 2-2 gives the volumes of the solid components, volumes of the open voids where coolant can directly flow, and volumes for the closed voids that are internal to the element.

2.3 FUEL DESIGN

The fuel cycle employs low-enriched uranium (LEU) and natural uranium (NU). The fissile fuel is a two-phase mixture of 19.8% enriched uranium in UQ.2901.63. The fertile fuel is the same as the fissile fuel, except that natural uranium is used rather than enriched uranium. The fissile fuel material is f m e d into kernels with a 350 pn diameter, and the fertile fuel material is formed into kernels with a 500 pm diameter. These fissile and fertile kernels are coated into particles, which are blended and bonded together with a carbonaceous binder into fuel compacts (Fig. 2-5).

The fuel compacts contained in the fuel holes have a 12.45 mm (0.49 in.) diameter with a length of 49.3 mm (1.94 in.). Each fuel compact is a mixture of fissile and fertile particles bonded by a carbonaceous matrix. These compacts are stacked in the fuel holes. The six stacks under each of the four dowels contain 14 fuel compacts; all other stacks contain 15 fuel compacts.

2.4 REFLECTOR ELEMENT DESIGN

The hexagonal reflector elements have a size, shape, and handling hole that are similar to the fuel elements, except that some of the reflector elements are half-height or three-quarter height. The inner (central) reflector includes 37 columns of hexagonal reflector elements. The outer side

2-5 DOE-HTGR-90406 / Rev. 0

W

2 I- ? ?

90

L-

8 Y w

0

J

JTDOWN HOLE

ROD HOLE

4 X $1.75 . DOWEL HOLE /- / /" HANOLING

186 X 9.50 J I I \6 X $.625 COOLANT HOLE

FUEL HOLE .740 TRIANGULAR -IF- PITCH

3

a

4 /

FIGURE 2-4 CONTROL OR RESERVE SHUTDOWN FUEL ELEMENT

2-7 DOE-HTGR-90406 / Rev. 0

TABLE 2-2 ELEMENT AND CORE VOLUMES

Standard ControVRSC Entire Volume Element, (m3) Element, (m3) Core, (m3) Fraction (%)

Solid Volumes Graphite Block 5.036-02 4.82 1-2/4.899-2 Fuel Rods 1.874-02 1.658-02 FBP Rods 3.70 1-04 3.701-04 Fuel & FBP Hole Plugs 1.7 15-04 1.524-04 Dowels 1.698-04 1.698-04 Total

Open Void Volumes Control Holes Coolant Holes Gaps Between Blocks Handling Hole Tooling Hole End Bevels Dowel Holes Total

0.0 1.66 1 -02 5.030-04 2.964-04 2.698-05 9.584-05 9.501-05

6.429-3/5.65 1-3 1.472-02 5.030-04 2.964-04 2.698-05 9.584-05 9.501 -05

41.875 55.71 15.224 20.25 3.109-01 0.4135 1.395-01 0.19 1.426-01 !LE 57.692 76.75

1.450 1 3.499 4.225-01 2.490-01 2.266-02 8.05 1-02 7.98 1-02 15,803

1.93 17.96 0.56 0.34 0.03 0.11 0.11

21.02

Closed Void Volumes Fuel Holes FBP Holes Total

Total Volume

1.829-03 1.626-03 2.20 1-04 2.201 -04

8.949-02 8.949-02

1.487 1.849-0 1 1.672

1.98 m 2.22

75.172 100.00 ~~

Number of Elements 600 120/120 840

2-8 DOE-HTGR-90406 / Rev. 0

FISSILE (URANIUM <20% ENRICHED)

FUEL COMPACT

V

FERTILE (NATURAL URANIUM)

FlGURE 2-5 FUEL ELEMENT COMPONENTS

2-9 DOE-HTGR-90406 / Rev. 0

reflector includes two rows of hexagonal reflector columns as shown in Fig. 2-2. Twenty-four of the elements in the inner row of the outer reflector also have a control rod channel as shown in Fig. 2-6. The control rod channel has a diameter of 102 mm (4 in.) and stops at an elevation just below the active core. The control rod channel is centered on the flat nearest the active core 102 mm (4.028 in.) from the center of the reflector element. The distance from the flat of the reflector block to the edge of the control rod channel is 27 mm (1.06 in.).

2.5 CONTROL MATERIAL

The core reactivity is controlled by a combination of fixed lumped burnable poison (FBP) compacts and movable control rods. The FBP consists of boron carbide (B4C) granules dispersed in graphite compacts. There is an average of 5.0 FBP rods (each rod is a stack of FBP compacts) per element in reload segment B of the initial core. The FBP compact diameter is 1 1.43 mm (0.45 in.). However, to simplify the benchmark calculations, it is assumed that there are seven FBP rods in each segment B element, with one FBP rod in the center of each 1/7 of the element, and that each of these FBP rods is of a smaller diameter to conserve the actual FBP volume per element.

The control rods are located in rows one and two of the core, and in the inner ring of the outer reflector (Fig. 2-2). The absorber compacts in the control rods consist of 40 wt % natural boron in B4C granules uniformly dispersed in a graphite matrix. The annular absorber compacts have an inner diameter of 52.3 mm (2.06 in.) and an outer diameter of 84.8 mm (3.34 in.). These compacts are enclosed in metal canisters for structural support and to limit oxidation of the boron carbide. The backup reserve shutdown control (RSC) is also available in the form of boronated pellets that may be released into channels in the active core. This RSC material is not included in the MHTGR benchmark problems.

2- 10 DOE-HTGR-90406 / Rev. 0

FUEL HANDLING I /- HOLE

- 14.172-

-@4.00 CONTROL ROD CHANNEL HOLE

- 3.841

31

FIGURE 2-6 REFLECTOR CONTROL ELEMENT

/

2-11 DOE-HTGR-90406 / Rev. 0

3. MHTGR BENCHMARK PROBLEMS

3.1 BENCHMARK CALCULATIONS TO BE PERFORIVED

A series of calculational benchmark problems for the MHTGR core are proposed, based on a 450 MW(t) annular core containing 84 columns. The selected problems use BOK atom densities to avoid the complexities of fuel depletion, and the nominal dimensions for core components used in previous MHTGR analyses. Six different benchmark models are specified :

Model 1 : Model 2 : Model 3 : Model 4 : Model 5 : Model 6 :

1-D Radial, Cylindrical Geometry 1-D Axial, Slab Geometry 2-D Radial, Hexagonal Geometry, 1 Hex per Element 2-D Radial, Hexagonal Geometry, 7 Hexes per Element 3-D Radial, Hexagonal Geometry, 1 Hex per Element 3-D Radial, Hexagonal Geometry, 7 Hexes per Element

The following benchmark cases are defined for each of the above models:

Case1 - Case2 - Case3 - Case4 -

cold reactor, all control rods out, dry hot reactor, all control rods out, dry cold reactor, all control rods out, with moisture ingress hot reactor, all control rods out, with moisture ingress

In addition, the following all-&-in cases are defined for the 2-D and 3-D models:

Case5 - Case6 - Case7 - Case8 -

cold reactor, all control rods inserted, dry hot reactor, all control rods inserted, dry cold reactor, all control rods inserted, with moisture ingress hot reactor, all control rods inserted, with moisture ingress

These benchmark calculations are summarized in Table 3-1. The nuclear analyst should attempt to calculate the power distribution and K-eff for as many of these benchmark problems as possible. By comparing the calculational results for the various cases, additional parameters are obtained, such as cold-to-hot temperature defect, control rod worth, and moisture ingress reactivity worth. These are the parameters that are most useful for validating the computer methods that are

3- 1 DOE-HTGR-90406 / Rev. 0

TABLE 3-1 MHTGR BENCHMARK CALCULATIONS TO BE PERFORMED

Benchmark Case : 1 2 3 4 5 6 7 8

Temperature : Cold Hot Cold Hot Cold Hot Cold Hot

All Control Rods Inserted: No No No No Yes Yes Yes Yes

With Moisture Ingress : No No Yes Yes No No Yes Yes

Hexes 1 Model Dimensions Geometry Element Benchmark Calcu lations Are to be Perfomd

1 1 Radial, cyl.

2 1 Axial, slab

3 2 Hexagonal

4 2 Hexagonal

5 3 Hex-2

6 3 Hex-Z

Yes Yes Yes Yes No NO No No

Yes Yes Yes Yes No NO NO No

1 Yes Yes Yes Yes Yes Yes Yes Yes

7 Yes Yes Yes Yes Yes Yes Yes Yes

1 Yes Yes Yes Yes Yes Yes Yes Yes

7 Yes Yes Yes Yes Yes Yes Yes Yes

3-2 DOE-HTGR-90406 / Rev. 0

used for physics design and analysis of the MHTGR. It should be noted that additional K-eff data may be obtained from the 0-D cross section calculations, and that, if necessary, the nuclear analyst can construct an R-2 model from the 1-D radial and 1-D axial models.

Analysts performing these benchmark calculations are to use the atom densities, temperatures, and dimensions provided in this document for their calculations. Items that are not specified, such as the neutron energy group structure, the source of the basic cross section data, the computer codes to be used, methods of including core leakages, etc., are to be selected by the analyst based upon what is deemed to be most appropriate for these benchmark problems.

3.2 CALCULATION OF CROSS SECTIONS

Microscopic cross sections for the core regions must be generated which account for the fuel particle and fuel rod heterogeneities at the various core temperatures. Microscopic cross sections for the reflectors must also be generated which account for the various reflector temperatures. The core and reflector cross sections must be generated for dry and moisture ingress conditions. Multi-group shielding factors must be accounted for in the calculation of the FBP and control rod cross sections. The data below should be sufficient to calculate these cross sections. If additional data is needed, it should be found in Section 2.

3.2.1 Core Cross Sect ions

Fuel particle and fuel rod heterogeneities must be accounted for in the calculation of the microscopic cross sections for the core. The nuclear analyst may use a two region model, where region 1 is the fuel rod, i.e. stack of fuel compacts, and region 2 represents the average amount of the fuel block per fuel rod. The average fuel rod for the entire core may be used in the calculation, or separate microscopic cross sections may be calculated for the two fuel segments, designated "A" and "B". The MHTGR core layout used for these benchmark problems is shown in Figure 3-1. This figure includes the locations of fuel segments A and B, but does not include the permanent reflector blocks. The data for these calculations is provided in Table 3-2.

Atom densities for the FBP are included in Table 3-2, and the nuclear analysts is encouraged to include, if possible, the FBP in the calculations of the core cross sections, provided that the effect of the FBP shielding also is included in the spectrum calculation. Calculation of core

3-3 DOE-HTGR-90406 / Rev. 0

0 n

Control Rod Location

0

0 RSC Location

Replaceable Reflector

Core Reload Segment A

Core Reload Segment 8

U

FIGURE 3-1 120' MODEL OF THE 84 COLUMN CORE

3 4 DOE-HTGR-90406 / Rev. 0

TABLE 3-2 DATA FOR THE CALCULATION OF DRY CORE CROSS SECTIONS

A v e w Ato m Densities U-235 (fissile particle) U-238 (fissile particle) U-235 (fertile particle) U-238 (fertile particle)

Boron (homogeneous) Carbon oxygen Silicon

B-10 (FBP)

&e. 1 Densitim Fissile U-235 Fissile U-238 Fertile U-235 Fertile U-238 Boron (homogeneous) Carbon oxygen Silicon

&g, 2 Densities B-10 (FBP) Boron (homogeneous) Carbon

Atom Densities in Fissile Kernels U-235 U-238 Carbon oxygen

Fuel s!a?XmL

l.OO362E-05 4.01382E-05 4.628 62E-07 6.382OOE-05 0.00000E+00 1.99968E-08 6.23773E-02 1.8657 1E-04 3.60864E-04

4.95552E-05 1.98 188E-04 2.28545E-06 3.15 12OE-04 2.13782E-08 6.66857E-02 9.2122OE-04 1.78182E-03

0.0 1.96462E-08 6.12832E-02

4.83921E-03 1.93537E-02 7.01 593E-03 3.94344E-02

Fuel saZumJ3

1 S299OE-05 6.1186OE-05 4.62862E-07 6.382OOE-05 2.596OOE-06 1.98986E-08 6.20709E-02 2.2945 8E-04 4.83 171E-04

7.5541OE-05 3.021 15E-04 2.28545E-06 3.15 12OE-04 2.072 15E-08 6.46372E-02 1.13298E-03 2.38572E-03

3.25 5 28E-06 1.96898E-08 6.141 9 1E-02

4.8392 1E-03 1.935 37E-02 7.0 1593E-03 3.94344E-02

Core A v e a 1.26676E-05 5.06621E-05 4.62862E-07 6.382OOE-05 1.298OOE-06 1.99477E-08 6.2224 1E-02 2.080 14E-04 4.22017E-04

6.2548 1E-05 2.50151E-04 2.28545E-06 3.15 1 20E-04 2.10498E-08 6.56615E-02 1.027 1 OE-03 2.08377E-03

1.62764E-06 1.9668OE-08 6.13511E-02

4.8392 1 E-03 1.93537E-02 7.0 1593E-03 3.94344E-02

3-5 DOE-HTGR-90406 / Rev. 0

TABLE 3-2 (Continued)

Atom Densities in Ferh 'le Kernels U-235 1.74189E-04 U-238 2.401 74E-02 Carbon 7.0 1593E-03 oxygen 3.94344E-02

Radius (cm) Region 1 (fuel rod) 0.6223 Region 2 (graphite block) 1.3828 Fissile kernels 0.0350 Fertile kernels 0.0500

Volume Fractio n3 Region 1 (fuel region) in cell Region 2 (graphite block) in cell Fissile kernels in fuel compact Fertile kernels in fuel compact

0.202526 0.797474

0.01024034 0.01312051

1.741 89E-04 2.40 174E-02 7.0 1593E-03 3.94344E-02

0.6223 1.3828 0.0350 0.0500

0.202526 0.797474

0.0 1561 020 0.01 3 1205 1

1.74 1 89E-04 2.40 174E-02 7 .O 1593E-03 3.94344E-02

0.6223 1.3828 0.0350 0.0500

0.202526 0.797474

0.0 1292527 0.01312051

3-6 DOE-HTGR-90406 / Rev. 0

cross sections with moisture ingress must include additional hydrogen and oxygen with 8.894E-04 and 4.447E-04 cell averaged atom densities to simulate lo00 Kg of H20 in the core. It should be assumed that this moisture does not enter the fuel rods, but is located entirely in region 2, so that the region 2 hydrogen and oxygen atom densities must be increased to 1.1 15E-03 and 5.576E-04, respectively, based on a region 2 volume fraction of 0.797474.

3.2.2 Reflect0 r cross secho ns

The reflectors in the benchmark problems are carbon, with impurities simulated by homogenized B-10. For the cold benchmark calculations, all reflectors are at 300 K. For the hot benchmark calculations, reflector regions are at 600,750,900, and 1050 K. Multi-group cross sections are to be calculated for the reflector regions using the atom densities in Table 3-3 for these temperatures under dry and moisture ingress conditions. These cross section calculations may use a fission source, a leakage source, or a mixture of the two. These reflector cross sections will be used for all of the benchmark problems.

3.2.3 Shielded FBP Cross Sectio nS

The microscopic cross sections for B-10 in the FBP must be generated with care due to the considerable self-shielding effect at the beginning of the initial cycle. The benchmark problems are based on a core at the beginning of the initial cycle, with two fuel segments (A and B) located as in Figure 3-1. Only the Segment B fuel elements contain FBP, with five FBP rods per element on average, giving an average FBP volume fraction of 0.004135, as in Table 2-2. However, for simplicity and consistency for these benchmark calculations, it shall be assumed that there is one FBP rod in the center of each subhex (1 / 7 of an element), so that there are the equivalent of seven FBP rods in each segment B fuel element for all MHTGR benchmark models. The radius of each of these seven FBP pins is reduced to maintain the same FBP volume fraction as with the five actual FBP pins in the element. All the benchmark problems should use the same shielded B-10 cross sections homogeneously distributed in a region, such as an element or subhex, to represent the FBP . This shielded B-10 cross section is calculated from a single higher order transport cell calculation using a 1-D annular cell model based on a standard Segment B subhex with an FBP rod at its center. The details for this 1-D model of the FBP cell are given in Table 3-4.

3-7 DOE-HTGR-90406 / Rev. 0

TABLE 3-3 DATA FOR CALCULATION OF REFLECTOR CROSS SECTIONS

Regions : RadialandAxial Permanent Pedaceab le Reflectors Reflectors

With moisture ingress : No Yes Nucli& Hydrogen 0.0 1.057-04 0.0 B- 10 2.7649OE-08 2.7649OE-08 5.78645E-08 Carbon 8.62465E-02 8.62465E-02 9.02493E-02 oxygen 0.0 5.28 6-05 0.0

Temperatures (K): 300,600,750, 300,600,750, 300,600 900, 1050 900, 1050

TABLE 3-4 DATA FOR 1-D FBP CELL CALCULATION

Cross-sectional area of subhex = 1 / 7 of the cross-sectional area of an element = 161.217 cm2 Cross-sectional area of FBP rod = (161.217) (0.004135) = 0.667 cm2

Region : This region represents : Radius (cm) Atom densities in region :

U-235 (fissile particle) U-238 (fissile particle) U-235 (fertile particle) U-235 (fertile particle) B- 10 (homogeneous) Carbon

Silicon oxygen

Region 1 Region 2 FBP Rod Remainder of subhex 0.4607 7.164

1 S3626E-05 6.14401E-05 4.64784E-07 6.408 5OE-05 1.99812E-08 6.20332E-02 2.3041OE-04 4.85 177E-04

6.278 1 1E-04 7.1 15 10E-02

3-8 DOE-HTGR-90406 / Rev. 0

3.2.4 Shielded Co ntrol Rod Cross Sectio nS

A macroscopic cross section for an isolated MHTGR control rod, whether located in a fuel or reflector element, should be calculated using the 1-D cell described in Table 3-5. The graphite sleeve in the model represents the extra graphite provided by designers which is placed at the edge of the control rod channel to strengthen the control rod element.

This 1-D cell model of the control rod may be used as part of a larger more detailed 1-D or 2-D transport cell which includes the fuel and/or reflector material that surrounds the control rod. The details of this more complex cell are left to the nuclear analyst. The fuel and reflector atom densities surrounding the control rod should be taken from the input data listed in Section 3.3.3 for the full "hex" block model or from Section 3.3.4, which uses 1 / 7 size "subhexes." The equivalent radius of a cylindricized subhex is 7.164 cm, and of a full element is 18.953 cm. These values should be used for the outer dimension of a 1-D control rod cell calculation, depending on whether it is for a control rod in a subhex or in a full element.

For simplicity, the control rod cell calculations should only be performed at 300 K under dry conditions, but the resulting control rod shielding factors should be applied to both hot and cold benchmark problems under dry and moisture ingress conditions. The rodded cases to be calculated in the 2-D and 3-D benchmark problems are only for fully rodded configurations. Partial rod insertions in the core do not need to be modeled. The final control rod cross sections will need to be shielded appropriately for the homogeneous regions being used, either one entire fuel or reflector element, or one 1 / 7 element size subhex (see Sections 3.3.3 through 3.3.6). The control rod cross section should be a macroscopic cross section with shielding factors applied, homogenized over the element or subhex, depending on the geometry being used in the MHTGR benchmark calculation. The homogenized macroscopic control rod cross section should include the shielded homogenized cladding around the B4C as well as the B4C.

3.3 SPECIFICATION OF MODELS FOR BENCHMARK CALCULATIONS

A series of calculational benchmark problems for the MHTGR core are proposed, based on a 450 MW(t) annular core containing 84 columns. The selected problems use BOIC atom densities to avoid the complexities of fuel depletion, and the nominal dimensions for core components used in previous MHTGR analyses. The benchmark calculations include six different core models:

3-9 DOE-HTGR-90406 / Rev. 0

IwQn 1

TABLE 3-5 DATA FOR 1-D CONTROL ROD CELL CALCULATION

. . SCnDhOn Void

Steel Cladding Void

Natural Boron Compact Void

Steel cladding Void

Graphite Sleeve

The atom densities used in this cell are as follows:

Region

2, 6

4

8

Outer Radius (em) 2.39 2.5 1 2.62 4.24 4.45 4.57 5.08 6.43

Volume Fraction 0.138 0.014 0.014 0.269 0.044 0.026 0.119 0,376 1 .ooo

Steel cladding around B4C Compact

Natural boron compact

Graphite Sleeve

3-10

Atom Density Jatoms /barn -cm)

Cr = 0.0171 Mn = 0.0006 Fe = 0.0391 Ni = 0.0272

B-Nat = 0.0357 Carbon = 0.0481 Carbon = 0.0826

DOE-HTGR-90406 / Rev. 0

Model 1 : Model 2 : Model 3 : Model 4 : Model 5 : Model 6 :

1-D Radial, Cylindrical Geometry 1-D Axial, Slab Geometry 2-D Radial, Hexagonal Geometry, 1 Hex per Element 2-D Radial, Hexagonal Geometry, 7 Hexes per Element 3-D Radial, Hexagonal Geometry, 1 Hex per Element 3-D Radial, Hexagonal Geometry, 7 Hexes per Element

All the models assume that the actual dimension for the outer radial and axial boundaries are located at the inside edge of the boronated steel pins located in the axial and radial reflectors. These six models are to use a zero boundary condition (flux = 0.0) at the outer radial and axial boundaries. The following data is provided for the above models :

(1) (2) Temperatures in Kelvin (3) Dimensions in cm

Beginning of initial cycle atom densities, properly homogenized in atoms / barn-cm.

Section 2 provides detailed dimensional data on the MHTGR reactor components for those who may wish to use more detailed geometric models, e.g. Monte Carlo calculations, for higher order comparisons to the benchmark problems defined in this section.

3.3.1 1-D Radial Model

The geometric locations of each region in the 1-D radial model are shown schematically in Figure 3-2. The geometry and homogenized atom densities, in atoms / barn-cm, are provided in Table 3-6. Heavy metal U-235 and U-238 nuclide densities are provided for both the fissile and fertile fuel particles. The outer boundary of the permanent reflector is specified to be 306.609 cm, which is the actual location of the inside edge of the boronated steel pins in the permanent reflector. The FBP B-10 is shielded burnable poison, calculated as described in Section 3.2.3, while the homogeneous B-10 is unshielded and represents impurities in the carbon. The hydrogen and oxygen atom densities for moisture ingress cases, with lo00 kg of water in the core, should be added as follows:

coreco mmnent - Regions Hvdrogen O x v m Active core 3,4, 5 8.894E-04 4.447E-04

Radial reflector 1, 2, 6, 7 1.057E-04 5.286E-05 Permanent Reflector 8 0.0 0.0

3-1 1 DOE-HTGR-90406 / Rev. 0

FIGURE 3-2 MODEL FOR 1-D RADIAL BENCHMARK CALCULATIONS

3-12 DOE-HTGR-90406 / Rev. 0

Region

Type:

Region : Nuclidu Fissile U-235 Fissile U-238 Fertile U-235 Fertile U-238

B-10 (homo.) Carbon oxygen Silicon

B-10 (FBP)

TABLE 3-6 DATA FOR 1-D RADIAL BENCHMARK

Core ComDonent

Inner removable reflector Inner removable reflector

Inner fuel ring Middle fuel ring Outer fuel ring

Outer removable reflector Outer removable reflector

Permanent reflector

Core Row 1

3

9.7 1808-06 3 -88659-05 5.63669-07 7.77 194-05 1.29800-06 1.97473-08 6.15989-02 2.06800-04 3.8 1267-04

Core &EL2

4

1.45561-05 5.82148-05 4.20 195-07 5.79369-05 1.29800-06 1.99866-08 6.23453-02 2.13744-04 4.54140-04

Pimensions (cml Inner outer

0.0 82.614 115.287 148.028 180.801 208.484 241.976 275.309

Core IbL3

5

82.614 115.287 148.028 180.801 208.484 241.976 275.309 306.609

300 300 300 300 300 300 300 300

900 1050 97 1 97 1 97 1 900 750 600

Replaceable Reflector Blacks Permanent Standard Sta n.+Control Reflector

6 8

1.31388-05 5.25465-05 4.24884-07 5.85 836-05 1.29800-06 2.00691-08 2.76490-08 2.65007-08 5.78645-08 6.26030-02 8.62465-02 8.26645-02 9.02493-02 2.03 25 6-04 4.22495-04

3-13 DOE-HTGR-90406 / Rev. 0

3.3.2 1-D Axial Model

Figure 3-3 provides the location of each region in the 1-D axial model of the MHTGR. The homogenized atom densities, in atoms / barn-cm, are provided in Table 3-7. The temperatures are listed in Table 3-8. The homogenized FBP B-10 should use the same shielded cross sections for all axial regions in the core as were utilized in Section 3.3.1 in the 1-D radial model. For moisture ingress problems, again assuming lo00 kg of water in the core, the following hydrogen and oxygen atom densities should be used :

Core Components Axial reflectors

Active core

AxialReAonS Hydro= Qiyga 1, 12 8.894E-04 4.447E-04

2 to 11 8.894E-04 4.447E-04

3.3.3 2-D Hexagonal Model

The 2-D hexagonal model uses one-third core symmetry (Figures 3-4 and 3-5) with atom densities @.able 3-9) homogenized over each hexagonal fuel or reflector element. Figure 3-4 provides the scheme by which the various elements are located geometrically in the model using the ring number, and the hex number within the ring. The composition types of each element in the one-third core model are shown in Figure 3-5. The temperature distribution in the 2-D hexagonal model is identical to that of the 1-D radial model, as given in Table 3-10. Control rod configurations are also defined for the 2-D hexagonal model in Table 3-10. In one-third geometry, this includes four control rods located in the fuel and eight control rods located in the outer reflector. The shielded macroscopic control rod cross sections (calculated using the higher order cell calculations discussed in Section 3.2.4) should be added to these locations. For the moisture ingress cases, with lo00 kg of water in the core, the hydrogen and oxygen atom densities are given below. It is assumed that no water enters the permanent reflector during a water ingress.

coreco mmnent - Ring: I&& Hvdrom Removablereflector 1, 2, 3 , 4 All 1.057E-04 5.286E-05

I t 7 1, 7 8 All 9

I t I 1

I t 11 11

t t 2 to 8, 10 to 16

2 to 6, 8 to 12

I t II

Active core 596 All 8.894E-04 4.447E-04 II 7 11 11

3-14 DOE-HTGR-90406

Dimension iU22 0.0

118.949

198.248

277.547

356.845

436.144

5 15.443

594.742

674.041

753.339

843.638

91 1.937

95 1.079

Region Number

1

2

3

4

5

6

7

8

9

10

11

12

Axial Region

Upper axial reflector

Core fuel layer 1

Core fuel layer 2

Core fuel layer 3

Core fuel layer 4

Core fuel layer 5

Core fuel layer 6

Core fuel layer 7

Core fuel layer 8

Core fuel layer 9

Core fuel layer 10

Lower axial reflector

F ' I G W 3-3 MODEL FOR 1-D AXIAL BENCHMARK CALCULATIONS

3-15 DOE-HTGR-90406

~~

TABLE 3-7 ATOM DENSITIES FOR 1-D AXIAL BENCHMARK

Type:

Axial Regions: Nuclides Fissile U-235 Fissile U-238 Fertile U-235 Fertile U-238 B-10 (FBP) B-10 (homo.) Carbon

Silicon oxygen

Type:

Axial Regions: Nuclides Fissile U-235 Fissile U-238 Fertile U-235 Fertile U-238 B-10 (FBP) B-10 (homo.) Carbon oxygen Silicon

Axial Reflecton

1, 12

2.20874E-08 6.8898OE-02

core Axial Layer 7

8

1.46 155E-05 5.84524E-05 4.62862E-07 6.382OOE-05 1.34992E-06 1.99477E-08 6.22241E-02 2.08014E-04 4.220 17E-04

core Axial vers 1 and 2 2and3

coreAxial

uE3 4

9.73945E-06 3.895 14E-05 4.62862E-07 6.382OOE-05 1.0384OE-06 1.99477E-08 6.22241E-02 2.08014E-04 4.22017E-04

core Axial Laver 8

9

1.2 1 838E-05 4.87272E-05 4.62862E-07 6.382OOE-05 1.34992E-06 1.99477E-08 6.22241E-02 2.080 14E-04 4.22017E-04

1.21 838E-05 4.87272E-05 4.628 62E-07 6.382OOE-05 1.53164E-06 1.99477E-08 6.22241E-02 2.08014E-04 4.220 17E-04

core Axial Lavers 9 and 10

10and 11

1.21 838E-05 4.87272E-05 4.628 62E-07 6.382OOE-05 1.0384OE-06 1.99477E-08 6.22241E-02 2.08014E-04 4.22017E-04

coreAxial Lavers 4. 5. 6

5, 6, and 7

1.46155E-05 5.84524E-05 4.62862E-07 6.3 82OOE-05 1.53 164E-06 1.99477E-08 6.2224 1E-02 2.08014E-04 4.22017E-04

3- 16 DOE-HTGR-90406 / Rev. 0

Re9on

1 2 3 4 5 6 7 8 9 10 11 12

TABLE 3-8 TEMPERATURES FOR 1-D AXIAL BENCHMARK

Core Component

Upper reflector Fuel Layer 1 Fuel Layer 2 Fuel Layer 3 Fuel Layer 4 Fuel Layer 5 Fuel Layer 6 Fuel Layer 7 Fuel Layer 8 Fuel Layer 9 Fuel Layer 10

Lower reflector

Dimensions (cm) Beeinning End

0.0 1 18.949 198.248 277.547 356.845 436.144 515.443 594.742 674.041 753.339 832.638 9 1 1.937

3-17

118.949 198.248 277.547 356.845 436.144 515.443 594.742 674.041 753.339 832.638 91 1.937 95 1.079

300 300 300 300 300 300 300 300 300 300 300 300

600 97 1 97 1 97 1 97 1 97 1 97 1 97 1 97 1 97 1 97 1 900

DOE-HTGR-90406 / Rev. 0

Element Designations :

where X = Ring Number Y = Hex Number Within Ring X

FIGURE 3-4 ELEMENT LOCATIONS FOR HEXAGONAL BENCHMARKS

3-18 DOE-HTGR-90406 / Rev. 0

STD CRD RSC REF PR = A = Segment A Fuel Element B = Segment B Fuel Element

FIGURE 3-5 ELEMENT TYPES FOR HEXAGONAL BENCHMARKS

3-19 DOE-HTGR-90406 / Rev. 0

TABLE 3-9 ATOM DENSITIES FOR 2-D HEXAGONAL BENCHMARK

Type : Segment : Ring : Hexes : Nud.iks Fissile U-235 Fissile U-238 Fertile U-235 Fertile U-238

B-10 (homo.) Carbon

Silicon

B-10 (FBP)

oxygen

Type : Segment : Ring : Hexes : Nuclides Fissile U-235 Fissile U-238 Femle U-235 Femle U-238

B-10 (homo.) Carbon

B-10 (FBP)

oxygen Silicon

Standard Fuel A 5

1, 5

8.1698OE-06 3.2673 8E-05 5.9 8 109E-07 8.2468OE-05

0.0 2.03294E-08 6.34149E-02 2.0198OE-04 3.54782E-04

Standard Fuel A 7

2, 4, 6, 9

1.06549E-05 4.26126E-05 4.34901E-07 5.99647E-05

0.0 2.03261E-08 6.34046E-02 1.85283E-04 3.67533E-04

Control Fuel A 5

3,7

7.22894E-06 2.891 1OE-05 5.29229E-07 7.29707E-05

0.0 1.91456E-08 5.97222E-02 1.787 19E-04 3.13924E-04

RSC Fuel A 7 11

9.42785E-06 3.77052E-05 3.848 16E-07 5.3059OE-05

0.0 1.9386OE-08 6.0472OE-02 1.63945E-04 3.25207E-04

3-20

Standard Fuel A 6

2, 4, 6, 10

1.18M3E-05 4.72093E-05 4.30101E-07 5.9302 8E-05

0.0 2.0299OE-08 6.33199E-02 1.93562E-04 3.9292OE-04

Standard Fuel B 5

4, 8

1.24539E-05 4.98074E-05 5.98109E-07 8.2468OE-05 2.596OOE-06 2.0221 1E-08 6.30768E-02 2.3689 1E-04 4.54343E-04

Control Fuel A 6 8

1.04449E-05 4.17725E-05 3,80569E-07 5.24733E-05

0.0 1.9 1 187E-08 5.96381E-02 1.7 127 1E-04 3.47670E-04

RSC Fuel B 5

2, 6

1.10197E-05 4.407 14E-05 5.29229E-07 7.29707E-05 2.596OOE-06 1.9293OE-08 6.0 18 18E-02 2.09610E-04 4.020 19E-04

DOE-HTGR-90406 / Rev. 0

TABLE 3-9 (Continued)

Type : Segment : Ring : Hexes : Nuclides Fissile U-235 Fissile U-238 Fertile U-235 Fertile U-238 B-10 (FBP) B-10 (homo.) Carbon

Silicon oxygen

Standard Fuel Control Fuel Standard Fuel RSC Fuel B B B B 6 6 7 7

195, 7 , 9 3 3, 8, 10, 12 5

1.79942E-05 7.1965 1E-05 4.30101E-07 5.93028E-05 2.596OOE-06 2.01427E-08 6.28323E-02 2.44004E-04 5.36773E-04

1.59219E-05 6.36774E-05 3.80569E-07 5.24733E-05 2.596OOE-06 1.89803E-08 5.92065E-02 2.15904E-04 4.74957E-04

Removable Reflector Elements : Ring 1, Hex 1 Ring 2, Hexes 1 ,2 Ring 3, Hexes 1,2,3,4 Ring 4, Hexes 1 to 6 Ring 8, Hexes 1, 3,4,7, 8, 10, 11, 14 Ring 9, Hexes 2 to 8,lO to 16

1.62422E-05 6.4958OE-05 4.34901E-07 5.99647E-05 2.596OOE-06 2.01 85OE-08 6.29643E-02 2.308 13E-04 4.97379E-04

1.437 17E-05 5.74772E-05 3.8 48 1 6E-07 5.3059OE-05 2.59600E-06 1.9261 1E-08 6.00822E-02 2.04232E-04 4.40099E-04

Atom Densities (at0 msh-cm) B-10 (homo.) Carbon

2.7649OE-08 8.62465E-02

Removable Reflector Control Elements : 2.56395E-08 7.9978OE-02 Ring 7, Hexes 1,7 Ring 8, Hexes 2, 5, 6, 9, 12, 13

Permanent Reflector, Ring 9, Hexes 1,9 Ring 10, Hexes 1 to 18

4.88999E-08 7.62674E-02

3-21 DOE-HTGR-90406 / Rev. 0

TABLE 3-10 TEMPERATURES AND CONTROL RODS FOR 2-D HEXAGONAL BENCHMARK

Inner reflector Inner reflector Inner fuel ring

Middle fuel ring Outer fuel ring outerreflector outer reflector Outer reflector Outer reflector

Permanent reflector Permanent reflector

Ring:

1 to 3 4 5 6 7 7 8 8 9 9 10

m All All All All

2 to 6, 8 to 12 1, 7

2 to 7,9 to 14 1, 8

2 to 8, 10 to 16 1,9 All

Control Rod Locatio n

Fuel - Segment A Segment A Segment B Segment A

Outer reflector Outer refiector Outer reflector Outer reflector Outer reflector Outer reflector Outer reflector Outer reflector

3-22

Ring

5 5 6 6 7 7 8 8 8 8 8 8

a?!d

300 300 300 300 300 300 300 300 300 300 300

3 7 3 8 1 7 2 5 6 9 12 13

lirst

900 1050 971 97 1 97 1 900 900 750 750 600 600

DOE-HTGR-90406 / Rev. 0

The nuclear analyst should use his own judgment in modeling the permanent reflector, so long as it is consistent with the 306.609 cm outer dimension given in Table 3-6. The option presented in Figure 3-5 models the permanent reflector as 20 columns in the 1/3 core layout. The permanent reflector atom densities in Table 3-6 were multiplied by the ratio of the permanent reflector volumes in the 1-D radial model compared to the 2-D hexagonal model (0.845075) to produce the permanent reflector atom densities in Table 3-9. This was done to conserve the total mass of the permanent reflector. The flat-to-flat dimension of each hexagon should be set equal to 36.09348 cm, consistent with the 14.212 inches in Table 2-1.

3.3.4 2-D Sub hex Mode 1

The 2-D subhex model uses the same hexagonal geometry as described in Section 3.3.3, except that each hexagonal fuel or reflector element is now modeled as seven separate "subhexes," as shown in Figure 3-6, with the flat-to-flat dimension of each subhex being 13.64394 cm. An added designator for subhex number is now used along with ring number and hex within ring number (as shown in Figure 3-4) to place subhex fuel and reflector types precisely in the 2-D geometric model. The subhex numbers 1 through 7 are located within every hexagonal element with the pattern shown in Figure 3-7. The atom density types used in the 2-D subhex model are given in Table 3-1 1. In this table, Figure 3-4 should be used to reference the ring and hex numbers, and Figure 3-7 should be used to reference the subhex numbers. The atom densities for each atom density type are given in Table 3-12. The nuclear analysts should use the same model for the permanent reflector in this subhex model as was used in the hexagonal model. Figure 3-7 and Table 3-1 1 assume that the permanent reflector is modeled by 20 columns in the 1/3 core layout. The atom densities for the subhexes in the replaceable and permanent reflectors are given in Table 3-13.

The temperam distribution and control rod locations are defined in Table 3- 14. The temperature distribution in the 2-D radial subhex model is the same as that presented in the previous section. In one-third geometry, the control rods are located as shown in Figure 3-7. Appropriately shielded control rod cross sections and atom densities should be added to these subhex locations based upon the higher order cell calculations discussed in Section 3.2.4. As in the previous section, the moisture ingress cases assume lo00 kg of water in the core, with the following hydrogen and oxygen atom densities :

3-23 DOE-HTGR-90406 / Rev. 0

HGURE 3-6 SUBHEX GEOMETRY USED TO MODEL AN ELEMENT

3-24 DOE-HTGR-90406 / Rev. 0

@ = ControlRodSubhex

0 = Reserve Shutdown Control Subhex

FIGURE 3-7 GEOMETRY FOR SUBHEX BENCHMARKS

3-25 DOE-HTGR-90406 / Rev. 0

TABLE 3-11 CORE ATOM DENSITY TYPES FOR 2-D SUBHEX BENCHMARK

Atom Den. Z h E

1

2

3

4

5

6

7

8

9

10

11

12

Reload Seement

A

A

A

A

A

A

B

B

B

B

B

B

5

5

6

6

7

7

5

5

6

6

7

7

Subhex

Standard

Control

Standard

Control

Standard

RSC

Standard

RSC

Standard

Control

Standard

RSC

3-26

Hexes

195 3 7

3 7

2, 4, 6, 10 8

8

2,49639 11

11

4, 8 2 6

2 6

1, 5,799 3

3

3, 8, 10, 12 5

5

Subhexes

All 1, 2, 3, 4, 6, 7 1, 2,394, 597

5 6

All 1, 2, 3, 4, 5, 7

6

All 1,2, 3,4, 5 , 7

6

All 1, 2, 3, 4, 5 , 7 1, 2, 3, 4, 5, 6

6 7

All 1, 2, 394,697

5

All 1, 2, 3, 4, 6, 7

5

DOE-HTGR-90406 / Rev. 0

Atom Den. Type Reload Segment

Ring Subhex Type

Nuclide Fissile U-235 Fissile U-238 Fertile U-235 Fertile U-238

B-impurity Carbon (total)

Oxygen Silicon

B-10 (FBP)

Atom Den. Type Reload Segment

Ring Subhex Type

Nuclide Fissile U-235 Fissile U-238 Fertile U-235

F Fertile U-238

(s\ B-impurity Carbon (total)

Oxygen 5 0 Silicon

8 Q E

B-10 (LBP)

\

F

TABLE 3-12 CORE ATOM DENSITIES FOR 2-D SUBHEX BENCHMARK

1 A 5

Standard

8.1 6980E-06 3.26738 E -05 5.981 09E-07 8.24680E-05 O.OOOOOE+OO 2.03294 E-08 6.341 49E-02 2.01 980E-04 3 54782 E-04

7 B 5

Standard

1.24539E-05 4.98074E-05 5.981 09E-07 8.24680E-05 2.59600E-06 2.0221 1 E-08 6.30768E-02 2.36891 E-04 4.54343E-04

2 A 5

Control Rod

1.58378E-06 6.33408E-06 1.1 5948E-07 1.59871 E-05 0.00000E+00 1.20429E-08 3.75660E-02 3.91 555E-05 6.87773E-05

8 B 5

R9c

2.41 429E-06 9.65557E-06 1.1 5948E-07 1.59871 E-05 2.59600E-06 1.37245E-08 4.281 16E-02 4.59232E-05 8.80780E-05

3 A 6

Standard

1.1 8043E-05 4.72093E-05 4.301 01 E-07 5.93028 E-05 0.00000E+00 2.0299OE-08 6.331 99E-02 1.93562E-04 3.9292OE-04

9 B 6

Standard

1.79942E-05 7.1 9651 E-05 4.301 01 E-07 5.93028E-05 2.59600E-06 2.01 427E-08 6.28323E-02 2.44004E-04 5.36 773 E-04

4 A 6

Control Rod

2.28835E-06 9.1 51 90E-06 8.33784E-08 1.14963E-05 0.00000E+00 1.20370E-08 3.75476E-02 3.75236E-05 7.61 707E-05

1 0 B 6

Control Rod

3.48833E-06 1.3951 OE-05 8.33784E-08 1.1 4963E-05 2.59600E-06 1.20062E-08 3.74515E-02 4.73021 E-05 1.04058E-04

5 A 7

Standard

1.06549E-05 4.261 26E-05 4.34901 E-07 5.99647E-05 0.00000E+00 2.03261 E-08 6.34046E-02 1.85283E-04 3.67533E-04

1 1 B 7

Standard

1.62422E-05 6.49580E-05 4.34901 E-07 5.99647E-05 2.59600E-06 2.01 850E-08 6.29643E-02 2.3081 3E-04 4.973 79 E-04

6 A 7

Is2

2.06554E-06 8.26080E-06 8.43090E-08 1.1 6246E-05 0.00000E+00 1.37454E-08 4.28767E-02 3.591 85E-05 7.1 2492E-05

1 2 B 7

FB2

3.1 4867E-06 1.25926E-05 8.43090E-08 1.1 6246E-05 2.59600E-06 1.371 75E-08 4.27898E-02 4.47449E-05 9.64209E-05

T A B U 3-14 TEMPERATURES AND CONTROL RODS FOR 2-D SUBHEX BENCHMARK

C m Cornuonea Location HfZ Subhex

Inner reflector Inner reflector Inner fuel ring

Middle fuel ring Outer fuel ring Outer reflector Outer reflector Outer reflector Outer reflector

Permanent reflector Permanent reflector

1 to 3 4 5 6 7 7 8 8 9 9 10

All All All All

2 to 6,8 to 12 197

2 to 7 , 9 to 14 1, 8

2 to 8, 10 to 16 1 9 9 All

All All All All All All All All All All All

300 300 300 300 300 300 300 300 300 300 300

900 1050 97 1 97 1 97 1 900 900 750 750 600 600

Control Rod Locan 'on Ring: Subhex

Fuel - Segment A Segment A Segment B Segment A

Outer reflector Outer reflector Outer reflector Outer reflector Outer reflector Outer reflector Outer reflector Outer reflector

5 5 6 6 7 7 a 8 8 8 8 8

3 7 3 8 1 7 2 5 6 9 12 13

5 6 5 6 3 4 3 4 4 4 5 5

3-29 DOE-HTGR-90406 / Rev. 0

Core Component Removable reflector

Active core

Hvdrog.enOxvg.en 1.057E-04 5.286E-05 8.894E-04 4.447E-04

3.3.5 3-D He xaeonal - Model

The 3-D hexagonal model uses the same radial geometry as the 2-D hexagonal model presented in Section 3.3.3, except with the axial dimension added. The axial geometry for the upper reflector, 10 layers of fuel, and lower reflector in the 3-D model uses the same axial dimensions as used in Section 3.3.2 for the 1-D axial model (Figure 3-3).

The upper and lower reflector regions in the 3-D model should use the same atom densities as were defmed in the 1-D axial model in Section 3.3.2. The 10 layers of fuel incorporate axial zoning of both the fissile heavy metal fuel particles and the FBP. The fertile heavy metal is not axially zoned. Therefore, the atom densities provided for the 2-D hexagonal model in Section 3.3.3 should be used for all 10 layers of fuel, except for the FBP and the U-235 and U-238 in the fissile particles, which must be multiplied by the axial zoning factors given in Table 3-13 for each axial fuel layer.

The control rod locations are also given Table 3-15. The control rod drives are designed so that at full retraction none of the natural boron compact material appears in the upper reflector region of the 3-D model. At full insertion, the boron compact resides completely in the 10 layers of fuel, but not in the upper or lower axial reflector regions.

The temperature distributions for the 3-D hexagonal model are as follows :

GiX Cold Hot

Comuonent - TemDeram All regions at 300 K Top reflector (above the core and radial reflectors) at 600 K Lower reflector (below the core and radial reflectors) at 900 K All core and radial reflector layers (over the height of the fueled core) use the radial temperatures defined in Section 3.3.3

Under moisture ingmss conditions, the 3-D hexagonal model must include the following hydrogen and oxygen densities :

3-30 DOE-HTGR-90406 / Rev. 0

TABLE 3-15 AXIAL ZONING FACTORS AND CONTROL RODS

FOR 3-D HEXAGONAL BENCHMARK

Axial Lay% r

2 3 4 5 6 7 8 9

10 (bottom)

1 (top)

Axial Regiw

Upper reflector Fuel layer 1 Fuel layer 2 Fuel layer 3 Fuel layer 4 Fuel layer 5 Fuel layer 6 Fuel layer 7 Fuel layer 8 Fuel layer 9 Fuel layer 10

Lower reflector

Fissile Particle U-235 and U-238

Zoning. Factor 0.769 0.769 0.962 1.154 1.154 1.154 1.154 0.962 0.962 0.962 1 .ooo

FBP B-10 Zoning. Factor

0.80 0.80 1.15 1.15 1.20 1.20 1.05 1.05 0.80 QAQ 1 .oo

Control Rod Boron Present All-Rods-In All-Rods-Out

No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No

3-31

No No No No No No No No No No No No

DOE-HTGR-90406 / Rev. 0

!Jm&wmm Radial reflectors over entire height Active core + axial reflectors

EbbasQ Oxvgen 1.057E-04 5.28 6E-05 8.894E-04 4.447E-04

3.3.6 3-D S u b b M a

The 3-D subhex model extends the 2-D subhex model presented in Section 3.3.4 in exactly the same manner as the 3-D hexagonal model of Section 3.3.5 extended the analogous 2-D model of Section 3.3.3. The zoning factors, temperatures, and rod location definitions used in Section 3.3.5 should also be applied in the 3-D subhex model. As in Section 3.3.5, the process is as follows:

1. Use the axial dimensions and upper and lower reflector atom densities from Section 3.3.2. 2. Use the radial hexagonal layout and atom densities from Section 3.3.4 for the 10 layers of

3. Use the axial zoning factors defined in Section 3.3.5 as multipliers for the fissile particle U-

4. Use the temperature, moisture ingress, and control rod data provided in Section 3.3.5.

fuel.

235 and U-238 and the FBP B-10 atom densities in fuel layers 1 through 10.

3-32 DOE-HTGR-90406 / Rev. 0